Speaking and listening skills are connected: usually, when you work on one you are automatically improving the other. It definitely helps to practise with either a native or a proficient speaker, but you might find not everyone has a clear accent - when it comes to natives, there are regional differences, and when it comes to non-natives, it depends on their natural abilities and how much work they've put into it (by "clear accent", I mean a more "standard" accent). It also helps a lot to get familiar with the IPA (there are slightly different versions for the British and the American varieties), and features of natural speech such as connected speech, intonation patterns, etc. If you don't have the chance to practise with someone, you may find lots of useful videos on YouTube to get a more accurate idea of how British and American people actually speak.
Good luck!